The precession of orbital and spin angular momentum vectors has been observed in a pump-probe study of the 4P fine-structure states of atomic potassium. A femtosecond pump pulse prepared a coherent superposition of the two fine-structure components. A time-delayed probe pulse then ionized the system after it had been allowed to evolve freely. Oscillations recorded in the ion signal reflect the evolution of the orientation of the orbital and spin angular momentum due to spin-orbit coupling. This interpretation gives physical insight into the cause of the half-period phase shift observed when the relative polarizations of the laser pulses were changed from parallel to perpendicular. Finally, it is shown that these changes in the orientation of the spin momentum vector of the system can be utilized to produce highly spin-polarized free electrons on the femtosecond scale